Two vectors vec{P} and vec{Q} are at an angle | vedclass

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(B) The unit vector $\hat{n}$ perpendicular to both vectors $\vec{P}$ and $\vec{Q}$ is defined as $\hat{n} = \frac{\vec{P} 	imes \vec{Q}}{|\vec{P}

Vedclass · Accepted Answer

$\frac{\hat{P} 	imes \hat{Q}}{\sin 	heta}$

Vedclass · Answer

(B) The unit vector $\hat{n}$ perpendicular to both vectors $\vec{P}$ and $\vec{Q}$ is defined as $\hat{n} = \frac{\vec{P} 	imes \vec{Q}}{|\vec{P} 	imes \vec{Q}|}$.We know that the magnitude of the cross product is $|\vec{P} 	imes \vec{Q}| = PQ \sin 	heta$.Substituting this into the formula,we get $\hat{n} = \frac{\vec{P} 	imes \vec{Q}}{PQ \sin 	heta}$.Since $\hat{P} = \frac{\vec{P}}{P}$ and $\hat{Q} = \frac{\vec{Q}}{Q}$,we can rewrite the expression as $\hat{n} = \frac{\vec{P}}{P} 	imes \frac{\vec{Q}}{Q} \cdot \frac{1}{\sin 	heta} = \frac{\hat{P} 	imes \hat{Q}}{\sin 	heta}$.

Two vectors $\vec{P}$ and $\vec{Q}$ are at an angle $\theta$ to each other. Which of the following is a unit vector perpendicular to both $\vec{P}$ and $\vec{Q}$?

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